There is no doubt that without observational data, modern cosmology is incomplete. From the detection of the cosmic microwave background radiation to the discovery of the late-time cosmic acceleration, we have witnessed how the observational data have been crucially important in the understanding of our Universe.
Whenever we talk about cosmology, the six parameter \(\Lambda \) CDM cosmological model under the assumptions of a positive cosmological constant, a pressure-less DM and a flat Universe, naturally enters into the picture because of its super agreement with a series of astronomical data. However, the true nature of DE and DM within this simplest cosmological scenario has remained one of the longstanding debates in cosmology. In addition to that, the assumption of a flat Universe has created a further debate in the scientific community. A series of recent articles have argued that the present observational data hint towards an evidence of a closed Universe [1]}, [2]}, [3]}, [4]}, [5]}. This evidence has sparked the entire scientific community because an evidence of a closed Universe increases the tensions in the key cosmological parameters and hence the flat \(\Lambda \) CDM cosmology is further challenged.
Generally, the curvature of the Universe is “assumed” to be zero when the cosmological models are analyzed. This is motivated because: (i) the inflationary paradigm have been tremendously successful demanding a spatially flat Universe, (ii) the observational data in the past preferred a small curvature of the Universe which is very close to zero, and further (iii) the inclusion of extra parameters in terms of the curvature parameter for instance, may increase the degeneracies in the parameters. However, over the last several years, the sensitivity of the astronomical data has improved a lot, and given such improvements,
it is very natural to allow the observational data to decide the nature of the curvature parameter. That means, the consideration of a flat Universe (i.e. \(\Omega _{K} =0\) ) while analyzing the cosmological models is not a very realistic assumption. We further comment that making \(\Omega _{K} =0\)  forcefully could bias the results and the intrinsic nature of the cosmological models may remain hidden forever [6]}, and at this stage where we have a large amount of astronomical data from various sources, having \(\Omega _{K} =0\)  is not expected.
